It is named after English mathematician Louis Napoleon George Filon, who first described the method in 1934.
[1] The method is applied to oscillatory definite integrals in the form: where
is either sine or cosine or a complex exponential that causes the rapid oscillation of the integrand, particularly for high frequencies.
values due to catastrophic cancellation;[3] Taylor series approximations must be in such cases to mitigate numerical errors, with
[2] Modifications, extensions and generalizations of Filon quadrature have been reported in numerical analysis and applied mathematics literature; these are known as Filon-type integration methods.
[6] Filon quadrature is widely used in physics and engineering for robust computation of Fourier-type integrals.
Applications include evaluation of oscillatory Sommerfeld integrals for electromagnetic and seismic problems in layered media[7][8][9] and numerical solution to steady incompressible flow problems in fluid mechanics,[10] as well as various different problems in neutron scattering,[11] quantum mechanics[12] and metallurgy.